Bring a large pot of water to a boil. Add pasta and cook, stirring occasionally, according to package directions. Stir in broccoli rabe (or spinach) during the last 2 to 3 minutes. Drain. Dry the pot.
Whisk broth and flour in a small bowl until smooth. Heat oil in the pot over medium-high heat. Add garlic and cook, stirring constantly, until fragrant, about 30 seconds. Add the broth mixture and bring to a simmer, whisking constantly, until it thickens, 3 to 4 minutes. Add beans, vinegar, salt and pepper and the pasta and broccoli rabe (or spinach). Cook, stirring, until the mixture is heated through, about 1 minute. Remove from the heat; add cheese, stirring until it melts. Serve immediately, topped with Toasted Breadcrumbs, if using.
To make toasted breadcrumbs, trim the crusts from 2 slices of whole-wheat sandwich bread. Tear the bread into pieces and process in a food processor into coarse crumbs. Toss breadcrumbs with 1 tablespoon extra-virgin olive oil and a pinch of salt in a small bowl. Cook in a large skillet over medium heat, stirring often, until golden and crisp, 3 to 5 minutes.